Low res texture in UV map with repetitive polygons
In the UV Editor (as shown in your picture), select one of the 'sides' (position the mouse cursor over one and hit L) then hit ctrl P - this will make it fill the image vertically at 64px high. Now scale it by half S (.5). Do the same with all the other 'sides' (not the top or bottom), they should now sit neatly one on top of the other, and be 32px high. 
Position the 2D Cursor on one of the vertices at the bottom of the 'sides' (select a vertex and hit shift S > Cursor to Selected),



and then set the pivot to 2D Cursor.



Now grab G the 'bottom' and position one of it's vertices on the 2D Cursor and then scale (S) until the next vertex lines up as shown.



Do the same with the 'top'. Now all resolutions should be the same and the sides will be 32px high. I hope this solves the problem.